MKE-FDocumentation / GNU Octave

Additional chapter 13 · interactive walkthrough

From element to global system

Three axial members, four degrees of freedom and the full sequence: element matrices → assembly → sparse storage → support → solution and reactions.

Reference contents

Model and degrees of freedom

Each node has one axial DOF. Numbering determines coefficient addresses in the global matrix.

Step 1 of 7

Structural model

Click an element to explore its matrix

Chain of three axial bar elements Four nodes, the first fixed, with a rightward axial force at the fourth. 1 2 3 4 u₁ = 0 u₂ u₃ u₄ e₁ e₂ e₃ P = 30 kN

Element e₁

k₁ = E₁A₁/L₁ = 10 kN/mm

Local DOFs [1, 2] global [u₁, u₂]
k(e) =
kN/mm

k(e) = (EA/L) · [[1, −1], [−1, 1]]

Global stiffness matrix K

K = 0
K is currently zero. The element map determines which four cells receive its contribution.
nonzero coefficient current contribution removed DOF
Elements assembled 0 / 3
System size to solve 4 × 4
State K not assembled

The full matrix remains unchanged until constraints are applied.